608 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 24, NO. 3, SEPTEMBER 2009 An Unsymmetrical Two-Phase Induction Motor Drive With Slip-Frequency Control Naser M. B. Abdel-Rahim and Adel Shaltout Abstract—This paper proposes a closed-loop control strategy to operate an off-the-shelf single-phase induction motor (IM) as a symmetrical two-phase IM. The proposed control strategy employs the SFC technique to independently control the stator currents of both the main and auxiliary windings, and make them follow a pre- defined sinusoidal waveform. Simulation and experimental results show that the proposed scheme is successful in operating the con- ventional single-phase IM as a symmetrical two-phase IM with fast dynamic and transient responses. In addition, the proposed control system achieves cost-effectiveness in both initial and running costs. Index Terms—Electric motor drive, single-phase induction mo- tor (IM), slip-frequency control (SFC), unsymmetrical two-phase IM. I. INTRODUCTION UMEROUS investigations have been carried out in the Fig. 1. Torque–speed characteristics are improved when the single-phase IM N literature to combine the merits of the polyphase induc- is operated as an unsymmetrical two-phase motor [8]. tion motors (IMs) (i.e., high performance) with those of the single-phase IMs (i.e., widespread use and availability) [1]–[7]. and [4], where the motor torque has been controlled by vary- These investigations have offered several control strategies and ing the PDA of the motor terminal voltages. This scheme has circuit topologies to operate the single-phase IM as a two-phase suffered from degraded efficiency when the PDA between the motor. The resulting two-phase IM drive has achieved cost- terminal voltages is small. effectiveness in both initial and running costs. Initial costs have Although the PDA control scheme has been successful in been reduced by: 1) dispensing the need to manufacture espe- operating the two-phase motor with a variable frequency, it is cially designed two-phase symmetrical motors and 2) increas- complex to implement. Moreover, high-torque pulsations re- ing the output power of the single-phase motor (see Fig. 1), sult when the phase angle between the motor terminal voltages thus allowing the use of a lower frame size to drive the same is other than 90◦. Torque pulsations become even more pro- load. Running costs have been reduced by reducing the motor nounced when the phase angle is small. losses and improving its power factor, thus enhancing the motor Space-vector closed-loop speed control of symmetrical two- efficiency [8]. phase IMs has been reported in [5]. Though successful in con- Open-loop speed control of the two-phase IM using two trolling the speed of the motor, this control scheme has not been single-phase half-bridge inverters operated in the square-wave optimal in driving the unsymmetrical two-phase IM since it ne- mode has been reported in [1] and [2]. With a square-wave volt- glects the zero-sequence components of the voltages/currents. age applied at the motor terminals, the motor terminal voltage Taking the zero-sequence components into account has com- and hence, line current had high harmonic content. This resulted plicated the implementation of the digital current controller [5]. in increased torque harmonics as well as reduced motor overall Rotor-flux-oriented space-vector control of unsymmetrical two- efficiency. To alleviate such problem, a phase difference angle phase IMs has been reported in [6] and [7]. Although this scheme (PDA) control employing the pulsewidth modulation (PWM) se- produces a high-dynamic-performance drive, yet it is compu- lective harmonic elimination technique has been reported in [3] tationally intense. Consequently, it requires high-power micro- controller or microprocessor for its implementation. Manuscript received September 6, 2006; revised January 8, 2009. Current In this paper, the slip-frequency control (SFC) technique is version published August 21, 2009. The work of N. M. B. Abdel-Rahim was supported by the United Arab Emirates University under Research Grant 04- proposed to independently control the stator currents of both 04-7-11/04. Paper no. TEC-00416-2006. the main and auxiliary windings, and make them follow a pre- N. M. B. Abdel-Rahim is with the Department of Electrical Engineering, determined sinusoidal wave. By maintaining certain operating Faculty of Engineering at Shoubra, Cairo, 11240, Benha University, Egypt (e-mail: [email protected]). conditions, the proposed control scheme reduces the inherent A. Shaltout is with the Department of Electrical Power and Machines, Cairo torque oscillations of the two-phase unsymmetrical IM, thus University, Giza 12613, Egypt (e-mail: [email protected]). making it behave like its symmetrical counterpart. Simulation Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. and experimental results show that this control scheme pro- Digital Object Identifier 10.1109/TEC.2009.2026599 vides excellent speed regulation with fast transient and dynamic 0885-8969/$26.00 © 2009 IEEE ABDEL-RAHIM AND SHALTOUT: AN UNSYMMETRICAL TWO-PHASE INDUCTION MOTOR DRIVE WITH SLIP-FREQUENCY CONTROL 609 Fig. 2. Cross section of the unsymmetrical two-phase motor. Fig. 3. Revolving fields in the unsymmetrical two-phase motor. (1) can be rewritten as responses. In addition, this control strategy limits the motor (N1 I1 + N2 I2 sin γ)cos(ωt + θ) line current during transient and dynamic stages to a maxi- 1 −N I cos γ sin(ωt + θ) mum of twice the full-load current, which reduces the rating √ 2 2 F (θ, t)= of the power inverter, and hence, its cost. To the best of the 2 (N1 I1 − N2 I2 sin γ)cos(ωt − θ) + authors’ knowledge, speed control of an unsymmetrical two- +N2 I2 cos γ sin(ωt − θ) phase IM using the SFC scheme has not been reported in the (3) literature. where the terms with cos(ωt + θ) and sin(ωt + θ) are the forward rotating fields and the terms with cos(ωt − θ) and sin(ωt − θ)are the backward rotating fields, and γ is the phase angle between II. BALANCED OPERATION OF THE UNBALANCED the current in the main winding and the current in the auxiliary TWO-PHASE MOTOR winding. The objective of this paper is to use the SFC scheme to re- In order to produce a circular rotating field in the motor air alize a high-performance two-phase IM drive, which makes the gap, and hence, eliminate the torque pulsations, the backward unsymmetrical (unbalanced) two-phase IM behave like its sym- components of the stator MMF should be canceled. This can be metrical (balanced) counterpart. To meet this objective, certain achieved if the following relationships between the current in operating conditions have to be satisfied first. the main winding and the current in the auxiliary winding are Fig. 2 shows a cross section of the two-phase unsymmetrical maintained: motor (conventional single-phase IM). The stator windings are I N = N I or I =a × I (4) unsymmetrical, but they are orthogonal with 90 electrical de- 1 1 2 2 2 1 grees apart. The stator MMF along a position defined by angle and θ (where θ = 0◦ defines the axis of the main winding) is given γ =90o by (5) N a = 1 . (6) F (θ, t)=F1 (θ, t)+F2 (θ, t) N2 = i N cos θ + i N cos(θ +90o ) (1) 1 1 2 2 Substituting (4) and (5) in (3) gives √ where F1 (θ, t) is the MMF produced by the main winding, Ff (θ, t)= 2N1 I1 cos(ωt + θ). (7) F2 (θ, t) is the MMF produced by the auxiliary winding, i1 and i are the currents in the main and auxiliary windings, 2 Equation (7) shows that the resultant motor MMF contains respectively, and N and N are the effective numbers of turns 1 2 only the forward revolving component F (θ, t). of the main and auxiliary windings, respectively. f Equation (1) shows that the MMFs produced by the main and III. EQUIVALENT CIRCUIT OF THE TWO-PHASE auxiliary windings have different magnitudes since the stator UNSYMMETRICAL IM UNDER SYMMETRICAL windings have different numbers of turns and parameters values. OPERATING CONDITIONS These unequal MMFs result in an elliptical MMF in the motor air gap, and hence, produce inherent torque pulsations. With both the auxiliary and main windings excited, the pul- For the main and auxiliary currents given by sating field produced by each winding of the unsymmetrical √ two-phase IM can be resolved into a forward and a backward i1 = I1max cos(ωt)= 2I1 cos(ωt) and revolving field. Consequently, there are four revolving fields in √ the air gap of the unsymmetrical two-phase IM, as shown in − − i2 = I2max cos(ωt γ)= 2I2 cos(ωt γ), (2) Fig. 3. 610 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 24, NO. 3, SEPTEMBER 2009 Fig. 4. Equivalent circuit of the unsymmetrical two-phase IM [9]–[11]. Fig. 4 shows the equivalent circuit of the unsymmetrical two- Referring to Fig. 4 and applying KVL for both the main and phase−−→ IM with both windings excited [9]–[11], where auxiliary windings gives E induced electromotive force (EMF) in the forward −−→ −−→ f 1 V = I (Z + Z + Z )+E + E (8) branch of the main winding by its forward revolving 1 1 1 f 1 b1 s1 s2 −−→ −−→ −−→ field; V2 = I2 (Z2 + Zf 2 + Zb2 )+Es3 + Es4 (9) Es1 induced EMF in the forward branch of the main winding by the forward revolving field of the aux- where Z1 is the series impedance of the main winding, which is given by −−→ iliary winding; E induced EMF in the backward branch of the main s2 Z1 = r1 + jX1 .